Image Formation at Plane and Spherical Refracting Interfaces

All flashcards

What equation describes image formation at a single spherical refracting surface?

$\frac{n_1}{d_o}+\frac{n_2}{d_i}=\frac{n_2-n_1}{R}$, where object and image distances are measured from the surface vertex.

What is the first focus of a spherical refracting surface?

The object position from which rays refract out parallel to the principal axis.

What is the second focus of a spherical refracting surface?

The image position for rays arriving parallel to the principal axis.

What does the paraxial approximation mean in spherical refraction?

It considers rays close to the principal axis, where the small-angle approximation is appropriate.

What does a negative image distance indicate under the stated convention?

The image is virtual.

Quiz questions

1. For a spherical interface with object-side index $n_1$, refracted-side index $n_2$, object distance $d_o$, image distance $d_i$, and radius $R$, which equation applies?Answer: $\frac{n_1}{d_o}+\frac{n_2}{d_i}=\frac{n_2-n_1}{R}$
2. For a spherical refracting surface, what happens to rays from an object at the first focus?Answer: They emerge parallel to the principal axis.
3. Under the stated sign convention for a spherical refracting surface, what does $d_i<0$ signify?Answer: The image is virtual.
4. When is the radius of curvature $R$ positive under the stated convention?Answer: When the surface is convex toward the object.
5. Why are the first and second focal distances generally different at a spherical refracting surface?Answer: Their expressions contain different refractive indices from the two media.